速度-费雪信息：经典与量子动力学中的混沌与不可逆性
Speed-Fisher Information: Chaos and Irreversibility in Classical and Quantum Dynamics
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中文总结 AI 辅助
本文提出速度-费雪信息作为统一框架，通过系统对慢驱动的敏感性表征经典与量子混沌，并关联不可逆熵产生，发现混沌表现为该信息随协议时间发散，且受低频谱权重控制，并识别出普朗克时间尺度下的独特量子标度。
中文摘要 AI 辅助
我们提出一个基于系统稳态对慢驱动敏感性的统一视角，用以理解经典与量子混沌。我们通过系统对平均协议速度的响应（称为“速度-费雪信息”）来探测这种敏感性，并将其与系统中的不可逆熵产生联系起来。我们证明，混沌动力学表现为速度-费雪信息随协议时间发散，且该响应受扰动低频谱权重的控制。这种混沌方法适用于经典和量子哈密顿系统，并自然扩展到非哈密顿经典流。此外，我们识别出一个量子区间，其时间尺度短于普朗克时间尺度，在该区间内速度-费雪信息表现出独特的量子标度行为。我们通过简单的经典和量子实例来说明这一框架。
英文摘要
We propose a unified perspective on classical and quantum chaos based on the sensitivity of a system's stationary states to slow driving. We probe this sensitivity via the system's susceptibility to the average protocol speed, which we call the ``speed-Fisher information," and relate it to irreversible entropy production in the system. We show that chaotic dynamics manifests as a divergence of the speed-Fisher information with the protocol time, and that this response is controlled by the perturbation's low-frequency spectral weight. This approach to chaos applies to both classical and quantum Hamiltonian systems, and naturally extends to non-Hamiltonian classical flows. Additionally, we identify a quantum regime at times shorter than the Planckian timescale, in which the speed-Fisher information exhibits a uniquely quantum scaling. We illustrate this framework with simple classical and quantum examples
发表机构
- Boston University（波士顿大学）
机构由 AI 辅助整理，请以论文原文为准。
